List of practice Questions

Two wires A and B are stretched by the same load. The radius of wire A is double the radius of wire B. The stress on the wire B as compared to the stress on the wire A is

When wavelength of light used in optical instruments A and B are 4500Å and 6000Å respectively, the ratio of resolving power of A to B will be

The ratio of radii of gyration of a ring to a disc (both circular of same radii and mass), about a tangential axis perpendicular to the plane is

The work done in blowing a soap bubble of radius \( R \) is \( W \). The work done in blowing a bubble of radius \( 2R \) of the same soap solution is

The light of wavelength \( \lambda \) incident on the surface of metal having work function \( \phi \) emits the electrons. The maximum velocity of electrons emitted is

A thin uniform rod has mass \( M \) and length \( L \). The moment of inertia about an axis perpendicular to it and passing through the point at a distance \( \frac{L}{3} \) from one of its ends, will be

The approximate value of the function \[ f(x) = x^3 - 3x + 5 \quad \text{at} \quad x = 1.99 \] is

The Cartesian coordinates of the point on the parabola \[ y^2 = x \quad \text{whose parameter is} \quad \frac{-4}{3} \] are

The equation of the tangent at \( P(-4, -4) \) on the curve \[ x^2 = -4y \] is

The angle between the line \[ \mathbf{r} = (i + j + k) + \lambda (3i + j + 3k) \] and the plane \[ \mathbf{r} \cdot (i + 2j + 3k) = 8 \] is

If \[ \frac{x}{\sqrt{1 + x^2}} + \frac{y}{\sqrt{1 + y^2}} = 0, \quad x \neq y, \text{ then } (1 + x^2)^2 \frac{dy}{dx} = \]

The sum of the cofactors of the elements of the second row of the matrix \[ \begin{pmatrix} 1 & 3 & 3 & 2 \\ -2 & 0 & 4 & 1 \\ 5 & 2 & 1 & 1 \end{pmatrix} \] is

If \( (a, -2a), \, a>0 \) is the midpoint of a line segment intercepted between the co-ordinate axes, then the equation of the line is

The direction cosines of a line which is perpendicular to lines whose direction ratios are \( 3, -2, 4 \) and \( 1, 3, -2 \) are

In a triangle \( ABC \) with usual notations, if \( \frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c} \), then the area of triangle \( ABC \) with \( a = \sqrt{6} \) is

Which among the following type of linkages is present in cellulose?

Which of the following is NOT present in baking powder?

A solution has an osmotic pressure of \( x \) kPa at 300K having 1 mole of solute in \( 10^{-5} \, \text{m}^3 \) of solution. If its osmotic pressure is reduced to \( \frac{1}{10} \) of its initial value, what is the new volume of solution?

In a quadrilateral \( ABCD \), \( M \) and \( N \) are the mid-points of the sides \( AB \) and \( CD \) respectively. If \( AD + BC = t \cdot MN \), then \( t = \)

Identify the product ‘A’ in the following reaction:
\text{Aniline} + (CH\(_3\)CO)\(_2\)O \(\xrightarrow{\text{pyridine}}\) A

Which among the following is used as refrigerants and for air conditioning?

What type of intermolecular force is present between magnesium chloride and water?

Which of the following salts contain interstitial water molecules in it?

Which among the following compounds belongs to lipids?

What is the effective atomic number of Zn in \([Zn(NH_3)_4]SO_4\)? (Atomic number of Zn = 30)